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" ANY two sides of a triangle are together greater than the third side. "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Pāgina 33
per John Playfair - 1832 - 333 pāgines
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The Living Age ..., Volum 281

1914
...shortest distance from one point to another is as "the crow flies"; and stated his proposition that any two sides of a triangle are together greater than the third. Ask the average boy to prove this as a general theorem : he will draw a perfect figure, measure the...
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The Monist, Volum 26

Paul Carus - 1916
...PROPOSITIONS. It has often been maintained that the twentieth proposition of the first book of Euclid — that two sides of a triangle are together greater than the third side — is evident even to asses. This does not however seem to me generally true. I once asked a coastguardsman...
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The Querrils

Stacy Aumonier - 1919 - 352 pāgines
...with a sense of form can see at a glance. I don't want a man to spend half the morning telling me that any two sides of a triangle are together greater than the third side. I also object to his method of proving that some quite obvious and useless proposition is wrong and...
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Plane Geometry

Walter Burton Ford, Charles Ammermann - 1923 - 232 pāgines
...meet at the point D within the triangle, and if AB > AC, prove that DB > DC. 40. Prove that the sum of any two sides of a triangle are together greater than the third side. [HiNT. Given the A ABC. To prove AB + AC > BC. Proof. Prolong BA to D making AD = AC. Join D to C....
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Space, Time and Gravitation: An Outline of the General Relativity Theory

Sir Arthur Stanley Eddington - 1923 - 218 pāgines
...geometry? Phys. Yes. Our experimental work proves it true. Rel. How, for example, do you prove that any two sides of a triangle are together greater than the third side? Phys. I can, of course, only prove it by taking a very large number of typical cases, and I am limited...
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Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - 1923 - 356 pāgines
...meet at the point D within the triangle, and if AB > AC, prove that DB > DC. 40. Prove that the sum of any two sides of a triangle are together greater than the third side. [HINT. Given the A ABC. To prove AB + AC > BC. Proof. Prolong BA to D making AD = AC. Join D to C....
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Educational Review, Volum 6

Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - 1893
...proved. Euclid demonstrates things more axiomatic by far. He demonstrates what every dog knows, that any two sides of a triangle are together greater than the third. Yet after he has finished his demonstration, that straight lines making with a transversal equal alternate...
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Educational Review, Volum 6

1893
...proved. Euclid demonstrates things more axiomatic by far. He demonstrates what every dog knows, that any two sides of a triangle are together greater than the third. Yet after he has finished his demonstration, that straight lines making with a transversal equal alternate...
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Non-Euclidean Geometry: A Critical and Historical Study of Its Development

Roberto Bonola - 1955 - 389 pāgines
...without it. Euclid demonstrated things more axiomatic hy far. He proves what every dog knows, that any two sides of a triangle are together greater than the third. Yet after he has finished his demonstration, that straight lines making with a transversal equal alternate...
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Texas State Journal of Medicine, Volum 9

1914
...who are distrustful of scientific methods. They will grudgingly admit that while, as a general thing, two sides of a triangle are together greater than the third side, yet after all we must be careful, as it is easy to carry mathematical reasoning too far.— Journal...
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